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Holt McDougal Geometry Unit 6
Polygons
Number of Sides |
Name of Polygon |
3 |
Triangle |
4 |
Quadrilateral |
5 |
Pentagon |
6 |
Hexagon |
7 |
Heptagon |
8 |
Octagon |
9 |
Nonagon |
10 |
Decagon |
12 |
Dodecagon |
n |
n-gon |
Vocabulary
Term |
Definition |
Vertex of the polygon |
The common endpoint of two sides of a polygon |
Diagonal |
A segment connecting any two nonconsecutive vertices of a polygon |
Regular polygon |
An equilateral and equiangular polygon (always convex) |
Concave polygon |
A polygon with parts of a diagonal on the exterior of the polygon |
Convex polygon |
A polygon with every part of the diagonals on the interior |
Rectangle |
A quadrilateral with four right angles |
Rhombus |
A quadrilateral with four congruent sides |
Square |
A quadrilateral with four right angles and four congruent sides; it is a parallelogram, a rectangle, and a rhombus |
Kite |
A quadrilateral with exactly two pairs of consecutive sides |
Trapezoid |
A quadrilateral with exactly one pair of parallel sides |
Base |
One of the parallel sides of a trapezoid |
Leg |
One of the nonparallel sides of a trapezoid |
Isosceles trapezoid |
A trapezoid in which the legs are congruent |
Midsegment of a trapezoid |
The segment whose endpoints are the midpoints of the legs of a trapezoid |
Theorems & Postulates
Name |
Theorem |
Polygon angle sum theorem |
The sum of the interior angle measures of a convex polygon with n sides is (n - 2)180 degrees. |
Polygon exterior angle sum theorem |
The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360 degrees. |
Trapezoid Midsegment Theorem |
The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases |
|
|
Formulas
Name |
Formula |
Sum of interior angle measures |
(n - 2)180 |
Midsegment of a trapezoid length |
1/2(base 1 + base 2) |
Midpoint Formula |
(x,y) = [(x1 + x2)/2], [(y1 + y2)/2] |
Distance formula |
√(x2 − x1)2+(y2 − y1)2 |
Properties of Parallelograms
If a quadrilateral is a parallelogram, then... |
Its opposite sides are congruent AND |
Its opposite angles are congruent AND |
Its consecutive angles are supplementary AND |
Its diagonals bisect each other. |
| |
If... |
One pair of opposite sides of a quadrilateral are parallel and congruent OR |
Both pairs of opposite sides of a quadrilateral are congruent OR |
Both pairs of opposite angles of a quadrilateral are congruent OR |
An angle of a quadrilateral is supplementary to both of its consecutive angles OR |
The diagonals of a quadrilateral bisect each other, |
then the quadrilateral is a parallelogram. |
Properties of Rectangles & Rhombuses
If a quadrilateral is a rectangle, then... |
It is a parallelogram AND |
Its diagonals are congruent. |
| |
If a quadrilateral is a rhombus, then... |
It is a parallelogram AND |
Its diagonals are perpendicular AND |
Each diagonal bisects a pair of opposite angles. |
Properties of Kites and Trapezoids
If a quadrilateral is a kite, then... |
Its diagonals are perpendicular AND |
Exactly one pair of opposite angles are congruent. |
| |
If a quadrilateral is an isosceles trapezoid, then... |
Each pair of base angles are congruent AND |
Its diagonals are congruent. |
| |
If... |
A trapezoid has one pair of congruent base angles OR |
A trapezoid has congruent diagonals, |
then the trapezoid is isosceles. |
|
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